OPERATION
RESEARCH
PART
– A
Q1. State the different
types of models used in operation research? Explain briefly the general method
for solving these O.R models?
Q2. Customer arrives at
sales counter by a poison process with a mean rate of 20 per hr. The time required
to serve a customer has an exponential distribution with a mean of 100 seconds.
Find the average waiting & queue length of customer.
Q3. Obtain the optimal
strategy for both persons & the value of game:
|
|
B1
|
B2
|
|
A1
|
1
|
-3
|
|
A2
|
3
|
5
|
|
A3
|
-1
|
6
|
|
A4
|
4
|
1
|
|
A5
|
2
|
2
|
|
A6
|
-5
|
0
|
Q4. Prepare network,
activity time estimates, determine the expected project completion time &
variance.
|
Activity
|
Time estimates (days)
|
||
|
to
|
Tm
|
tp
|
|
|
1-2
|
5
|
8
|
17
|
|
1-3
|
7
|
10
|
1
|
|
2-3
|
3
|
5
|
7
|
|
2-4
|
1
|
3
|
5
|
|
3-4
|
4
|
6
|
8
|
|
3-5
|
3
|
3
|
3
|
|
4-5
|
3
|
4
|
5
|
5. What is queuing theory?
Discuss the service mechanism in queuing theory.
PART – B
Q1. Determine a sequence
for the 5 jobs that will minimize the elapsed time.
|
Job
|
1
|
2
|
3
|
|
|
|
A
|
5
|
1
|
9
|
|
|
|
B
|
2
|
6
|
7
|
|
|
Q2. What is meant by
optimality test in a transportation problem? How would you determine
whether a given
transportation solution is optimal or not?
Q3. OR advocates a system
approach and its procedure is concerned with optimization. Discuss.
Q4. Discuss the importance
and applications of PERT and CPM in project planning and control.
Q5. Write short notes on
n- Johnson’s algorithm for n jobs m machines
PART - C
Q1. Solve the following
transportation problem by VAM:
|
|
1
|
2
|
3
|
Supply
|
|
1
|
5
|
1
|
7
|
10
|
|
2
|
6
|
4
|
6
|
80
|
|
3
|
3
|
2
|
5
|
15
|
|
Demand
|
70
|
20
|
50
|
|
Q2. Write short notes on :
a) Failures in replacement
theory.
b) Decision tree analysis.
Q3. The maintenance cost
& resale value per year of machine whose purchase price is Rs 7000 is given
below:
Yr 1 2 3 4
Maintenance
cost 900 1200 1600 2100
Resale
value 4000 2000 1200 600
When should the machine be
replaced?
Q4. Specify the
characteristics of M/M/1 queue model.
Q5. Discuss the following
terms in game theory: Saddle point; Pure strategy; Two person zero sum game;
Principle of dominance.
CASE STUDY – I
A firm manufactures three
products A,B,C the profits are RS 3, Rs 2, & Rs 4respectively. The firm has
two machines M1& M2 and below given is the required processing time in
minutes for each machine on each product
|
MACHINE
|
PRODUCT
|
||
|
A
|
B
|
C
|
|
|
M1
|
4
|
3
|
5
|
|
M2
|
2
|
2
|
4
|
Machines M1 & M2 have
2000 & 2500 machine minutes respectively. The firm must manufacture 100
A’s, 200 B’s & 50 C’s, but not more than 150 A’s. Set up an LPP to maximize
profits.
CASE STUDY
A fruit vendor purchases
fruits for Rs 3 a box and sells for Rs 8 a box. The high markup reflects the perish
ability of the fruit and the great risk of stocking it., the product has no
value after the first day it is offered for sale. The vendor faces the problem
of how many boxes to order for tomorrow’s business. A 90 day observation of the
past sales gives the following information.
|
Daily Sales
|
No. of days sold
|
Probability
|
|
10
11
12
13
Total
|
18
36
27
9
90
|
.20
.40
.30
.10
1.00
|
Determine the number of
boxes he should order to maximize its profit. Also find the expected monetary
value and regret table.
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